Showing 2 results for Differential Quadrature Method.
A. Karami Mohammadi, N. Aleali,
Volume 34, Issue 1 (7-2015)
Abstract
: In this paper, a nonlinear model of clamped-clamped microbeam actuated by electrostatic load with stretching and thermoelastic effects is presented. Free vibration frequency is calculated by discretization based on DQ method. Frequency is a complex value due to the thermoelastic effect that dissipates the energy. By separating the real and imaginary parts of frequency, quality factor of thermoelastic damping is calculated. Both stretching and thermoelastic effects are validated against the results of the reference papers. The variations of thermoelastic damping versus elasticity modulus, coefficient of thermal expansion and geometrical parameters such as thickness, gap distance, and length are investigated and these results are compared in the linear and nonlinear models for high values of voltage. Also, this paper shows that since for high values of electrostatic voltage the linear model reveals a large error for calculating the thermoelastic damping, the nonlinear model should be used for this purpose.
H. Salehipour,
Volume 41, Issue 1 (9-2022)
Abstract
In this paper, static buckling of homogeneous beams coated by a functionally graded porous layer with different boundary conditions is investigated based on the Timoshenko beam theory. The principle of virtual work has been used to obtain the governing equations. Two different methods, namely analyticalsolution and numerical solution are used to solve the governing equations and extract the buckling force. The governing equations are coupled as a series of ordinary differential equations. In the analytical solution, these equations are first uncoupled using a series of mathematical operations, and are then solved. The obtained solution has a series of parameters and unknown constants. Using the boundary conditions at the boundaries of the beam, a homogeneous system of equations is extracted, from which the axial buckling force is obtained. In the numerical solution, the generalized differential quadrature method is used to solve the static equations. Finally, the numerical results are presented and the effects of various parameters such as thickness to beam length ratio, porous layer thickness, porosity parameter, etc. on the buckling of the beam are investigated. Comparison of the results obtained from the two analytical and numerical solution methods confirms the accuracy and validity of both methods.
